Question

please answer with easy steps

Answer 1

In ∆ ABC,


$\Rightarrow$∠ABC = 90° [ Angle in a semicircle ]


Also,


$\Rightarrow$∠CAB + ∠ACB + ∠ABC = 180° [ Angle Sum Property ]


$\Rightarrow$∠CAB + ∠ACB + 90° = 180°


$\Rightarrow$∠CAB + ∠ACB = 180° - 90° = 90°


$\Rightarrow$∠CAB = 90° - ∠ACB ______ [1]


Now,


$\Rightarrow$∠OAT = 90°


Also, ∠OAT = ∠CAB + ∠BAT


∴∠CAB + ∠BAT = 90°


$\Rightarrow$ 90° - ∠ACB + ∠BAT = 90° [ From [1] ]


$\Rightarrow$ -∠ACB + ∠BAT = 90° - 90° = 0


$\Rightarrow$∠BAT = ∠ACB


Hence Proved !!

Answer 2

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